Pricing the CBOT T-Bonds Futures

Abstract

The aim of this paper is to investigate the theoretical and empirical pricing of the Chicago Board of Trade (CBOT) Treasury-bond futures. The difficulty to price it arises from its multiple interdependent embedded delivery options, which can be exercised at various times and dates during the delivery month. We consider a continuous-time model with a continuous underlying factor (the interest rate), moving according to a Markov diffusion process consistent with the no-arbitrage principle. We propose a numerical pricing model that can handle all the delivery rules embedded in the CBOT T-bond futures, interpreted here as an American-style interest-rate derivative. Our pricing procedure combines dynamic programming, finite-elements approximation, analytical integration and fixed-point evaluation. Numerical illustrations, provided under the Vasicek (1977) and Cox-Ingesoll-Ross (1985) models, show that the interaction between the quality and timing options in a stochastic environment makes the delivery strategies complex, and not easy to characterize. We also carry out an empirical investigation of the market in order to verify whether short traders in futures contracts are exercising the strategic delivery options skillfully and optimally or if they are under-utilizing them. To do so, we price the futures contract under the Hull-White (1990) model. Empirical results show that futures prices are generally undervalued, which means that the market overvalues the embedded delivery options. According to our findings, observed futures prices are on average 2% lower than theoretical futures prices over the 1990-2008 time period, priced two months prior to the first day of delivery months.